Solar CookingJordan Englünd

Heat Transfer

April 2008

Project Description

Cooking with the sun:

Easy and fun to do,but how long does ittake to cook a hotdog with the sun tothe propertemperature of 150 degrees F?

Proof of concept

This technology

is used all over the

world for solar

power plants.

Approach to problem

Because of the complications of having a variable convective coefficient, the temperature range (55 K) has been divided into 5 smaller temperature ranges (11 K).

The convective coefficient will be assumed to be constant over those ranges.

Problem Setup

For each temperature range, the net energy transferred to the hot dog due to radiation from the sun and by free and natural convection will be calculated.

Using lumped capacitance, the time needed to transfer enough energy to make the temperature change was calculated.

The time needed for each of the 5 temperature ranges was added to get the total time to cook the hot dog.

Radiation

qin = αGAdish – EAsurface

= αGAdish – εEbAsurface

= αGAdish – εEbAsurface

= αGAdish – εσTfAsurface

where…α = 0.675 1 (see figure to the right)

G = 1226 W/m2 (see problem 12.7)

ε = 0.825 1

Tsun = 5800 K

1 http://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=en

Convection

Heat transfer from convection was calculated by combining free convection and forced convection. Forced convection was assumed to be due to a

light summer breeze of 1 mph.

Is it necessary to combine forced and free?Gr = 3e4

Re2 = 8e5

Forced convection was more significant, but both were included for accuracy (using equation 9.64 with transverse flow).

Free | Forced

q = haveAdog(Tdog-T∞)

NuD comes from equation 9.34 for a horizontal cylinder.

q = haveAdog(Tdog-T∞)

NuD comes from the Churchill equation (7.54):

Wind speed: a light breeze of 1 mph.

www.eng.nus.edu.sg

Properties

Hot Dog: Length = 17 cmDiameter = 3.25 cmkdog = 0.52 1

ρdog = 930 2

cp,dog = 2340 3

Initial temp: 75 FFinal temp: 150 FTemp steps: 11 K

Environment:Wind: 1 mph

horizontal breezeOutside temp: 75 FDish diameter: 0.3 m

at opening (parabolic)Sun: 5800 K, at 30

degrees from vertical (summer conditions)

1 http://books.google.com/books?id=OOo98fhmEqoC&pg=RA1-PA233&lpg=RA1-PA233&dq=emissivity+of+meat&source=web&ots=KhcL8UveHW&sig=YlQk49B5tsKK-5So62tDcpQkJS0&hl=en 2 http://asae.frymulti.com/abstract.asp?aid=15409&t=23 http://www.engineeringtoolbox.com/specific-heat-capacity-food-d_295.html

Results

Using lumped capacitance the time needed to make each temperature step was calculated from the net heat transferred to the hot dog and then summed.

Time to fully cook the hot dog:

10 minutes and 7 seconds

Appendix – Excel Calculator